Free-form optics have been proven to be a very powerful and efficient illumination strategy with applications ranging from automotive and architecture illumination to laser beam shaping. State of the art free-form optics design methods assume that the light has zero étendue, which is for example given if it is emitted from a point source or perfectly collimated. In some cases, this assumption is not valid and designing free-form optics with a zero-étendue method and using a non-zero étendue source will result in a blurring effect for sharp edges in the irradiance pattern. In previous work1, we derived an integral formulation for the irradiance distribution on a target screen for a non-zero étendue source. Furthermore, we showed for a 2D-application that it is possible to combine this irradiance calculation method with a surface optimization routine to obtain free-form optics that also take into account a non-zero étendue. As a continuation, we extend this approach to three dimensions. To this end, we show how the integral formulation can be approximated numerically in three dimensions and we present an optimization method for the free-form optics. We demonstrate the performance of the algorithm by using two different test cases. For the second test case, we additionally present how the achieved irradiance distribution varies with the étendue of the source.
Designing freeform optical surfaces with a large number of degrees of freedom has been a field of extensive research and development. Several design methods have been proposed. Starting point in the design process often is an idealized light source that has zero étendue (e.g. point source or collimated light). With this assumption the solution is unique and corresponds to the solution of an equation of Monge-Ampère type. We propose a method to solve the Monge-Ampère equation on convex bounded domains by using triangle meshes and by minimizing the difference between prescribed and actual target light distribution which is computed by tracing rays through the optical surface. The mathematical solution has to comply with two conditions: the boundary of the source domain has to be mapped onto the boundary of the target domain and the solution has to be convex. The boundary condition problem is solved using a signed distance function that is computed in advance by a fast marching algorithm. The actual light distribution is computed by tracing rays along the triangle nodes and computing the light irradiance on the target by dividing the light flux through a triangle by its mapped area on the target. Under certain conditions this is also an approximate solution to the Optimal Transportation Problem with quadratic cost.
further shape or diffuse the light distribution (e.g. in non-imaging luminaires or automotive headlights). While the
geometry can be described in a parametric form by mapping the micro-optical features onto an underlying smooth
freeform surface, ray-tracing an optical system composed of NURBS or polynomial B-spline surfaces for each
optimization step can be costly.
We report on an extension of the previously published two-step freeform optics tailoring algorithm using a Monge-Kantorovich mass transportation framework. The algorithm's ability to design multiple freeform surfaces allows for the inclusion of multiple distinct light paths and hence the implementation of multiple lighting functions in a single optical element. We demonstrate the procedure in the context of automotive lighting, in which a fog lamp and a daytime running lamp are integrated in a single optical element illuminated by two distinct groups of LEDs.
We present a model and results of simulations and experiments investigating the L-I characteristics of electrically pumped (EP-) VECSELs in the single- and multi-mode regime. In our model we use a mode expansion ansatz to treat the electromagnetic field inside the VECSEL cavity. The eigenmodes of the passive cavity are computed using the bidirectional beam propagation method (BDBPM) to solve the Helmholtz equation. The BDBPM allows us to account for the complex refractive index distribution within the semiconductor heterostucture, composed of approximately thousand interfaces along the optical axis in addition to lateral refractive index variations in oxide-confined devices as well as the macroscopic external cavity. We simulate the time evolution of the modal powers of several transverse modes and the spatial distribution of the inversion carriers in the quantum well plane. Therefore we solve an differential equation system composed of multimode rate equations and the carrier diffusion equation. With this ansatz we are able to identify cavity geometries suitable for single-mode operation assuming typical current profiles that are taken from photoluminescence measurements of the devices under investigation. Furthermore, we identify effects limiting the single-mode efficiency, such as poor gain and mode matching, reabsorption in unpumped regions of the quantum wells or enhanced carrier losses due to strong spatial hole burning. Critical parameters of the equations, such as optical losses, injection effciency, carrier recombination constants and gain parameters are obtained from experiments, microscopic models and literature. The simulation results are compared to experimental results from EP-VECSELs from Philips Technologie GmbH U-L-M Photonics.